15. A landscaper uses a wheelbarrow to move soil to a certain region of the garden. A
wheelbarrow can hold approximately 6 cubic feet of soil. The soil is damped out into a pile
that makes the shape of a cone. The landscaper calculates that once the pille has a diameter
of 13 foet and a height of 3 feet, there will be sufficient soil for the project How maty
wheelbarrow loads of soil are needed for this project?

Answer:

Tom worked approximately 8 overtime hours in the given pay period.

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

a² = b² + c² - 2bc cos A

a² = (7√3)² + (√6)² - 2(7√3)(√6) cos 45°

a² = 49 × 3 + 6 - 14√18 × (√2)/2

a² = 153 - 42

a² = 111

a = √111

a = √n = √111

n = 111

Step-by-step explanation:

a = k/m    or       ma = k    

using 4 and 9     4* 9 = k = 36

then the equation becomes:

    ma = 36    

  using a = 6

      6 * m = 36     shows m = 6 kg

The points where the rate of change of f(x) equal to zero are A, C and E

From the question, we have the following parameters that can be used in our computation:

The graph

The point where the rates is 0 are the points where movement is at a constant

using the above as a guide, we have the following:

The points are A, C and E

Hence, the point where the rates is 0 are A, C and E

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Answer:

x = -1, 1

Step-by-step explanation:

The function h(x) is given below:

[tex]\displaystyle{h(x)=\dfrac{x-9}{x^2-1}}[/tex]

The denominator must not equal to 0. Therefore,

[tex]\displaystyle{x^2-1\neq 0}[/tex]

Solve the inequality; factor the expression:

[tex]\displaystyle{(x-1)(x+1) \neq 0}[/tex]

Hence,

[tex]\displaystyle{x \neq 1,-1}[/tex]

Therefore, x = -1, 1 both are not in the domain of h.

Step-by-step explanation:

We can use the equation h(t) = -4.9t^2 + vt + h0, where h0 is the initial height of the rock, v is the initial velocity and t is time in seconds, to solve the problem.

h0 = 43 meters (the top of the cliff)

v = 11 meters per second (upwards direction)

To find the time when the rock is 10 meters from ground level, we set h(t) = 10 meters and solve for t:

10 = -4.9t^2 + 11t + 43

0 = -4.9t^2 + 11t + 33

Solving this quadratic equation, we get t = 4.04 seconds or t = 1.37 seconds.

Since the rock is thrown upwards, it will be 10 meters from ground level twice - once on the way up and once on the way down. We can discard the negative time answer as that would correspond to when the rock is thrown from the ground.

Therefore, the rock will be 10 meters from ground level after 4.04 seconds (on the way down).

The correct time(s) when you are at the same height as the top of the tower are approximately -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so on.

To find the time or times during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower, we can solve the given equation for t.

320 = -197cos(π/15(t)) + 246

First, let's isolate the cosine term:

-197cos(π/15(t)) = 320 - 246

-197cos(π/15(t)) = 74

Next, divide both sides by -197:

cos(π/15(t)) = 74 / -197

Now, we can take the inverse cosine (arccos) of both sides to solve for t:

π/15(t) = arccos(74 / -197)

To isolate t, multiply both sides by 15/π:

t = (15/π) * arccos(74 / -197)

Using a calculator to evaluate the arccosine term and performing the calculation, we find the value(s) of t:

t ≈ -1.57, 1.57, 4.71, 7.85, 11.00, ...

These values represent the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower. Note that time is typically measured in hours, so these values can be converted accordingly.

In light of this, the appropriate time(s) when you are at the same altitude as the tower's peak are roughly -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so forth.

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Answer:

12

Step-by-step explanation:

[tex]\frac{3}{4}[/tex](x - 3) - [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]

We are looking at the denominators of 4, 2 and 3.  We are looking for the least common multiple.  If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.

4,8,12

2,4,6,8,10,12

3,6,9,12

the lowest number that we see on all three lists is 12.

If the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.

Given that the required reserve ratio is 30 percent and all figures are in billions, the following table shows the total reserves, excess reserves, and required reserves:

Required reserve ratio 30% Checkable deposits $140Billion Reserves required (30% of checkable deposits)$42Billion Reserves held $51Billion Excess reserves held $9Billion Loans outstanding $109Billion Total Securities $100Billion Total Property $10Billion Total Assets $260Billion Stock shares $130Billion Total liabilities $130Billion Net worth (total assets - total liabilities) $130Billion.

Therefore, the total reserves held is $51 billion, and the reserves required is 30% of $140 billion, which is $42 billion.

This implies that the excess reserves are $9 billion.The maximum amount the commercial banking system can lend out is $51 billion minus $42 billion, which is $9 billion.

This indicates that if the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.

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Answer:  Choice A

The single squiggly symbol means "similar".

A squiggly line over top an equals sign is the congruence symbol.

Answer:

Hope this helps and have a nice day

Step-by-step explanation:

To find the probability that a student is accepted at FSU or accepted at UF, we can use the concept of conditional probability and the law of total probability.

Let's denote the events as follows:

A: Accepted at FSU

B: Accepted at UF

We need to find P(A or B), which can be calculated as the sum of the probabilities of each event minus the probability of their intersection:

P(A or B) = P(A) + P(B) - P(A and B)

Given the information provided, we can calculate the probabilities:

P(A) = 0.4 (40% chance of being accepted at FSU)

P(B|A) = 0.6 (60% chance of being accepted at UF if accepted at FSU)

P(B|A') = 0.9 (90% chance of non-acceptance at UF if not accepted at FSU)

P(A and B) = P(A) * P(B|A) = 0.4 * 0.6 = 0.24 (probability of being accepted at both FSU and UF)

Now we can substitute these values into the formula:

P(A or B) = P(A) + P(B) - P(A and B)

= 0.4 + (1 - 0.4) * P(B|A') - P(A and B)

= 0.4 + 0.6 * 0.9 - 0.24

= 0.4 + 0.54 - 0.24

= 0.7

Therefore, the probability that a student is accepted at FSU or accepted at UF is 0.7, or 70%.

Step-by-step explanation:

Y = 2 sin 3x            '2' is the amplitude

                      ( 'sin x' usually has amplitude of '1'...then you multiply it by '2' )

                                '3' changes the period

Answer:

Step-by-step explanation:

he amplitude of the sinusoid graph y=2sin3x is 2.

Answer:

cos Z = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

cos Z = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{YZ}{XZ}[/tex] = [tex]\frac{10}{26}[/tex] = [tex]\frac{5}{13}[/tex]

Answer:

BC = 24 units

Step-by-step explanation:

This is an isosceles triangle which always has:

In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.

Thus, we can find x by setting CA and BA equal to each other:

(3x - 15 = x + 33) + 15

(3x = x + 48) - x

(2x = 48) / x

x = 24

Thus, x = 24

Since the length of BC is x and x = 24, BC is 24 units long.

The calculated value of m in the triangular prism is 13

From the question, we have the following parameters that can be used in our computation:

The triangular prism

Where, we have

Volume = 1170

The volume of the triangular prism is calculated as

Volume = Base area * Height

So, we have

1/2 * m * 18 * 10 = 1170

Evaluate the products

This gives

90m = 1170

So, we have

m = 13

Hence, the value of m is 13

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Answer:

C.  [7.6, 10.6]

Step-by-step explanation:

To calculate the confidence interval for the mean number of misspelled words in the student population, we can use the confidence interval formula:

[tex]\boxed{CI=\overline{x}\pm z\left(\dfrac{s}{\sqrt{n}}\right)}[/tex]

where:

Given values:

The standard deviation is the square root of the variance:

[tex]s=\sqrt{s^2}=\sqrt{12.25}=3.5[/tex]

The empirical rule states that approximately 99.7% of the data points will fall within three standard deviations of the mean.

Therefore, z-value for a 99.7% confidence level is z = 3.

Substituting these values into the formula, we get:

[tex]CI=9.1\pm 3\left(\dfrac{3.5}{\sqrt{49}}\right)[/tex]

[tex]CI=9.1\pm 3\left(\dfrac{3.5}{7}\right)[/tex]

[tex]CI=9.1\pm 3\left(0.5\right)[/tex]

[tex]CI=9.1\pm 1.5[/tex]

Therefore, the 99.7% confidence limits are:

[tex]CI=9.1-1.5=7.6[/tex]

[tex]CI=9.1+1.5=10.6[/tex]

Therefore, the confidence interval for the mean number of misspelled words in the student population is [7.6, 10.6].

Answer: B. The minimum y-value of g(x) is -3.

Step-by-step explanation:

Based on the given functions:

f(x) = 3 - 3

g(x) = 7x² - 3

The y-value of f(x) is constant at -3, regardless of the value of x. Therefore, f(x) does not have a minimum y-value, and option A is incorrect.

The y-value of g(x) is determined by the quadratic term 7x². Since the coefficient of x² is positive (7), the parabola opens upwards, indicating that g(x) has a minimum y-value. To find the minimum value of g(x), we can look at the vertex of the parabola, which occurs when x = -b/2a in the quadratic equation ax² + bx + c. In this case, a = 7 and b = 0, so the vertex is at x = -0/2(7) = 0. Substituting x = 0 into g(x), we find: g(0) = 7(0)² - 3 = -3 Therefore, the minimum y-value of g(x) is -3, and option B is correct.

Option C, stating that g(x) has the smallest possible y-value, is incorrect because the y-value of g(x) can be larger than -3 depending on the value of x.

Option D, stating that f(x) has the smallest possible y-value, is incorrect because f(x) does not have a minimum y-value as it is constant at -3.

Therefore, the correct answer is B. The minimum y-value of g(x) is -3.

The correct value of volume of the pyramid is 48 cubic inches.

To find the volume of the solid oblique pyramid, we can use the formula V = (1/3) * Base Area * Height. The base of the pyramid is a triangle, and the height is given as 6 inches.The formula for the area of a triangle is (1/2) * base * height. In this case, the base length is 8 inches and the height is 6 inches. Base Area = (1/2) * 8 * 6 = 24 square inches

Now, we can calculate the volume of the pyramid:

V = (1/3) * Base Area * Height

V = (1/3) * 24 * 6

V = 48 cubic inches

Therefore, the volume of the pyramid is 48 cubic inches.

None of the provided options (a, b, c, d) match the calculated volume of 48 cubic inches. Please double-check the given options or provide the correct options for further comparison.

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Answer:

x = 1307

Step-by-step explanation:

We have tan(α) = opposite/adjacent

⇒ tan(48.4) = 1472/x

⇒ x = 1472/tan(48.4)

⇒ x = 1306.9

⇒ x = 1307

Answer:

Step-by-step explanation:

To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.

The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.

Using the Pythagorean theorem, we can find the length of the remaining side TH:

TH^2 = TE^2 - HE^2

TH^2 = 4^2 - 4^2

TH^2 = 16 - 16

TH^2 = 0

TH = 0

Therefore, the length of side TH is 0.

The total volume of the dill spears is approximately 160 cm³.

To find the total volume of the dill spears, we'll need to determine the volume of the pickling liquid and subtract it from the total volume of the jar.

Given information:

Base area of the jar = 45 cm²

Height of the jar = 13 cm

Pickle juice drained = 160 cm³

First, let's calculate the volume of the jar:

The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.

The base area of the jar is given as 45 cm², which means πr² = 45.

So, we can find the radius (r) of the base using the formula r = √(45/π).

Let's calculate the value of r:

r = √(45/π) ≈ 3.79 cm

Now we can find the volume of the jar:

V_jar = πr²h

= π(3.79)²(13)

≈ 1818.73 cm³

Next, let's calculate the volume of the pickling liquid:

Given that 160 cm³ of pickle juice was drained, the volume of the pickling liquid is equal to the volume of the jar minus the volume of the drained pickle juice.

V_pickling_liquid = V_jar - 160

≈ 1818.73 cm³ - 160 cm³

≈ 1658.73 cm³

Finally, to find the total volume of the dill spears, we need to subtract the volume of the pickling liquid from the volume of the jar:

Total volume of dill spears = V_jar - V_pickling_liquid

≈ 1818.73 cm³ - 1658.73 cm³

≈ 160 cm³

Therefore, the total volume of the dill spears is approximately 160 cm³.

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Answer:

We have similar triangles.

7/3.5 = 5/x

2 = 5/x, so x = 2.5

Sampling based upon equal probability is called d. Simple random sampling. The correct answer is d. Simple random sampling.

Simple random sampling is a sampling technique where each individual in the population has an equal probability of being selected for the sample. It is based on the principle of equal probability, ensuring that every element has the same chance of being chosen. This method involves randomly selecting samples without any specific grouping or stratification.

Cluster sampling involves dividing the population into clusters or groups and randomly selecting entire clusters for inclusion in the sample. It does not guarantee equal probability for individual units within each cluster.

Probability sampling is a general term that encompasses different sampling methods, including simple random sampling, stratified random sampling, and cluster sampling. It refers to sampling techniques that rely on random selection and allow for the calculation of probabilities associated with sample estimates.

Stratified random sampling involves dividing the population into distinct strata based on certain characteristics and then selecting samples from each stratum in proportion to their representation in the population. It does not guarantee equal probability of selection for all individuals.

Systematic sampling involves selecting every kth individual from a population list after randomly selecting a starting point. It does not guarantee equal probability of selection for all individuals.

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Answer:

The domain of this function is all real numbers.

Triangle PQR is similar to triangle P”Q”R” because the rotation and dilation transformations preserve the shape and angles of the original triangle.

The rotation simply changes the orientation of the triangle, but the angles and side lengths remain the same. The dilation scales all the side lengths by a factor of 9, which preserves the ratios of the side lengths and the angles of the original triangle.

Since similarity of two triangles is defined as the correspondence between the angles of one triangle to the angles of another triangle, and the ratio of the lengths of the corresponding sides is constant, PQR is similar to P”Q”R” because the angles of PQR and P”Q”R” are congruent, and the ratio of the lengths of the corresponding sides is the same. This means that PQR and P”Q”R” have the same shape and are therefore similar.

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(a) 58 = 2(w + 5 + w)

(b)  I. The width of the rectangle is 12 cm.

II. The length of the rectangle is 17 cm.

III. The area of the rectangle is 204 cm².

Let's solve the problem step by step:

(a) To write an equation for the perimeter of the rectangle, we know that the perimeter is the sum of all four sides. Let's denote the width of the rectangle as "w" (in cm). Given that the length is 5 cm more than the width, the length would be "w + 5" (in cm). The formula for the perimeter is:

Perimeter = 2(length + width)

Substituting the values, we have:

58 = 2(w + 5 + w)

Simplifying the equation, we get:

58 = 2(2w + 5)

(b) Now let's solve for the width and length of the rectangle:

I. To find the width, we solve the equation:

58 = 2(2w + 5)

Dividing both sides by 2, we get:

29 = 2w + 5

Subtracting 5 from both sides, we have:

24 = 2w

Dividing both sides by 2, we find:

w = 12 cm

Therefore, the width of the rectangle is 12 cm.

II. To find the length, we substitute the value of the width into the equation:

Length = w + 5 = 12 + 5 = 17 cm

Therefore, the length of the rectangle is 17 cm.

III. The area of the rectangle can be calculated using the formula:

Area = length × width

Substituting the values, we have:

Area = 17 cm × 12 cm = 204 cm²

Therefore, the area of the rectangle is 204 cm².

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